Single actuator Wiper design to wipe a surface area

I'm given this problem to solve with the assumption as stated above. The answers need not be logical as long as the linkage mechanism can be simulated. I've attempted the question using Mercedes Mono Wiper mechanism but only manage to cover 41% given the width of the wiper. May I ask if there are any ideas or reference for me to look into to cover as much of the area as possible while satisfying all the criteria?

Area of parallelogram surface area=1,600,000 mm2
Area of covered area assume swiping half circle=663,747 mm2

I broke down the question into 2 parts which is moving the wiper platform left and right+moving the wiper platform up and down. So like a bouncing DVD logo we see on TV, eventually it will travel through all possible locations on the screen.
To move the wiper left and right

1. The actuator will produce a rotation motion along x axis.
2. The rotating Traverse Roll will move the platform left and right.
Reference:

Now we need to move the wiper up and down.

3. Using the Whitworth quick return mechanism to produce a left to right movement.
4. The left right movement produced will operate and move the wiper attached to the scissors table up and down.
I've made a crude sketch of what I have came up with. However I have a problem linking the rotating circle to the actuator.
Things I considered are
1) belt (not possible because the platform is moving from left to right constantly)
2) rack and pinion (the movements of the wiper is constant this way and will not be able to cover the whole wiper surface.)My concept of this would be to operate like a bouncing ball in a box. Eventually the ball will cover all the possible spots on the screen.

Need help connecting from the actuator to making the circle on a left right moving platform rotate. Thank you